Fast & accurate emulation of two-body scattering observables without wave functions

Abstract

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial $K$ or $T$ matrix constructed from a small number of exact solutions to the Lippmann--Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.

arXiv comment9 pages, 6 figures; minor updates, close to published version

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• Bayesian parameter estimation in $\chi$EFT using Hamiltonian Monte Carlo
• Excited states from eigenvector continuation: the anharmonic oscillator
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• Inference of the low-energy constants in $\Delta$-full chiral effective field theory including a correlated truncation error
• Nuclear-matter saturation and symmetry energy within $\Delta$--full chiral effective field theory
• A Complex Scaling Method for Efficient and Accurate Scattering Emulation in Nuclear Reactions
• Reduced basis emulation of pairing in finite systems
• Floating block method for quantum Monte Carlo simulations
• Greedy Emulators for Nuclear Two-Body Scattering
• Perspectives on few-body cluster structures in exotic nuclei
• Wave-packet continuum discretisation for nucleon-nucleon scattering predictions
• IMSRG-Net: A machine learning-based solver for In-Medium Similarity Renormalization Group
• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
• Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description
• Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory
• Active learning emulators for nuclear two-body scattering in momentum space
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation
• Ab initio study of the neutron and Fermi polarons on the lattice
• Uncertainty Quantification in Breakup Reactions